Question

prove that:-

√[(1+sinx)/(1+sinx)]+√[(1-sinx)/(1+sinx)] = 2secx.

Answer 1

$\huge \bf{HEY \: FRIENDS!!}$


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$\huge \bf \underline{Here \: is \: your \: answer↓}$

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$\huge \boxed{Prove \: \: that:-)}$

$\bf = > \sqrt{ \frac{1 + \sin(x) }{1 - \sin(x) } } + \sqrt{ \frac{1 - \sin(x) }{1 + \sin(x) } } = 2 \sec(x) .$


$\huge \boxed{Solving \: LHS:-)}$


$\bf = \sqrt{ \frac{1 + \sin(x) }{1 - \sin(x) } } + \sqrt{ \frac{1 - \sin(x) }{1 + \sin(x) } } .$


$\bf \: = \frac{ \sqrt{1 + \sin(x) } }{ \sqrt{1 - \sin(x) } } + \frac{ \sqrt{1 - \sin(x) } }{ \sqrt{1 + \sin(x) } } .$


$\bf = \frac{1 + \sin(x) + 1 - \sin(x) }{ \sqrt{(1 - \sin(x))(1 + \sin(x)) } } .$


$\bf = \frac{2}{ \sqrt{(1 - { \sin }^{2}(x) } } .$


$\bf = \frac{2}{ \sqrt{ { \cos }^{2}(x) } } .$


$\bf = \frac{2}{ \cos(x) } .$


$\bf = 2 \sec(x) .$


$\huge \boxed{LHS = RHS.}$


✅✅ Hence, it is proved✔✔.



$\huge \boxed{THANKS}$


$\huge \bf \underline{Hope \: it \: is \: helpful \: for \: you}$

Answer 2

Answer:

√1 +sin/1-sin× 1+sin /1+sin x +√1-sin/1+sin × 1-sin/1-sin

1+sin/cos + 1-sin/cos

2/cos x = 2sec x